On the sign problem in 2D lattice super Yang--Mills

Abstract

In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.

22 pages, 12 figures

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• Phase Structure of Lattice N=4 Super Yang-Mills
• Progress and prospects of lattice supersymmetry
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• Lattice formulation of three-dimensional $\mathcal{N}=4$ gauge theory with fundamental matter fields
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• A Euclidean Lattice Formulation of D=5 Maximally Supersymmetric Yang-Mills Theory
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• Nonperturbative phase diagram of two-dimensional $\mathcal{N}=(2,2)$ super-Yang--Mills